For ethanol, C2H5OH, which is mixed with gasoline to make the fuel gasohol, H°f = -277.63 kJ/mol. Based upon data in Table 6.2, and that the density of ethanol is 0.787 g•cm-3, the number of kilojoules released by burning completely 2.40 gallons of ethanol is ?
*Table 6.2 states that the enthalpy of C2H5OH is -277.63
I converted 2.4 gallons to cc and obtained 9085 cc but you should confirm that.
9085 x 0.787 g/cc = ? grams.
?g/molar mass = moles = x
Energy released is
277.63 kJ/mol x x mol = zz.
To determine the number of kilojoules released by burning completely 2.40 gallons of ethanol, we need to follow these steps:
Step 1: Convert the volume of ethanol from gallons to liters.
1 gallon is approximately equal to 3.78541 liters. Therefore, 2.40 gallons is equal to:
2.40 gallons * 3.78541 L/gallon = 9.07 L
Step 2: Calculate the mass of ethanol.
We can calculate the mass of ethanol using its density. The density of ethanol is given as 0.787 g/cm³. Therefore, the mass of 9.07 L (or 9070 cm³) of ethanol can be calculated as:
Mass = Density * Volume
Mass = 0.787 g/cm³ * 9070 cm³ = 7134.29 g
Step 3: Calculate the number of moles of ethanol.
Using the molar mass of ethanol, which is:
Molar mass of C2H5OH = 12.01 g/mol (C) + 2 * 1.01 g/mol (H) + 16.00 g/mol (O) = 46.07 g/mol
The number of moles of ethanol is:
Moles = Mass / Molar mass
Moles = 7134.29 g / 46.07 g/mol = 155 moles (approximately)
Step 4: Calculate the energy released by burning completely 1 mole of ethanol.
The enthalpy of formation of ethanol (ΔH°f) is given as -277.63 kJ/mol. This value represents the energy released when 1 mole of ethanol is formed. In this case, we want to calculate the energy released by burning 155 moles of ethanol. Therefore, the energy released by burning 1 mole of ethanol is also the energy released by burning 155 moles of ethanol.
Step 5: Calculate the energy released by burning 2.40 gallons of ethanol.
Energy released = Energy released by burning 1 mole of ethanol * Number of moles
Energy released = -277.63 kJ/mol * 155 moles = -43,025.65 kJ
Therefore, the number of kilojoules released by burning completely 2.40 gallons of ethanol is approximately -43,026 kJ.
To find the number of kilojoules released by burning 2.40 gallons of ethanol, we need to follow a series of steps:
Step 1: Convert gallons to liters
One gallon is approximately equal to 3.78541 liters. Therefore, we can convert 2.40 gallons to liters by multiplying it by the conversion factor:
2.40 gallons × 3.78541 liters/gallon = 9.085 liters
Step 2: Convert liters to grams
To convert liters to grams, we need to use the density of ethanol. The density of ethanol is given as 0.787 g/cm³. We can convert the volume in liters to grams using the following formula:
mass = volume × density
mass = 9.085 liters × 0.787 g/cm³ = 7.155595 grams
Step 3: Convert grams to moles
To convert grams to moles, we need to know the molar mass of ethanol (C2H5OH). The molar mass can be calculated by summing the atomic masses of each element in the compound:
C (12.01 g/mol) × 2 + H (1.00784 g/mol) × 6 + O (15.999 g/mol) + H (1.00784 g/mol) = 46.07 g/mol
Now we can convert grams to moles using the molar mass:
moles = mass / molar mass = 7.155595 grams / 46.07 g/mol = 0.155356 moles
Step 4: Calculate the energy released
The enthalpy of formation (ΔH°f) for ethanol is given as -277.63 kJ/mol. The negative sign indicates that this amount of energy is released when one mole of ethanol is formed. Since we have 0.155356 moles of ethanol, we can calculate the energy released by multiplying the moles by the enthalpy of formation:
energy released = moles × ΔH°f = 0.155356 moles × -277.63 kJ/mol = -43.139 kJ
Therefore, burning completely 2.40 gallons of ethanol releases approximately 43.139 kJ of energy.